Obviously TfL can't do anything about a US bank/ card issuer having policies that lose them money, but the turnstiles are aware that they have no (passenger accessible) inputs and so
they do not ask for a signature.
EMV lets the card (or in this case maybe a phone) and the terminal (in this case a turnstile inside the station, or a reader on a bus) negotiate what to do, the issuer may not be involved since it's possible they'll agree the entire transaction needn't yet involve the issuer. This is related to one bug in EMV, you could intercede in the middle to tell the card "It's OK, no need for a PIN" and also tell the terminal, "Yes, the PIN supplied was correct" and since the terminal doesn't know the correct PIN you've now got a shim that allows you to use the wrong PIN with a stolen card†.
Anyway, TfL terminals aren't going to agree to signatures. So, if your card really does only work with a signature then you can't use the turnstiles, along with presumably many other modern conveniences.
† There are obvious technical fixes. But the fixes cost money, and fraud is a cost banks can pass to their customers, guess what happens next.